Think you know the whos, whats, and whys of American race relations in the north in the 1950s? Think again. Adherence to the kind of convention that might inform your impressions is all but nonexistent in Luck of the Irish, Kirsten Greenidge’s new play that just opened at the Claire Tow Theater as part of Lincoln Center Theater’s LCT3 series. In following the intertwining fortunes of two Boston families, one black and one white, starting in the late 1950s and ending some 45 years later, it seeks to challenge at every turn the notions we thought we had about how African-Americans asserted and positioned themselves in the years before the Civil Rights Era. As a result, it’s never less than interesting, though it’s held back by its playwright’s insistence on employing the tired devices in some areas she eschews in others.

At least in its main storyline, Luck of the Irish is a swirling chronicle centered on that most stationary of objects: a house. Specifically, the home of Lucy and Rex Taylor, a well-to-do black couple who inhabited it for decades before passing away recently and leaving their granddaughters, Hannah and Nessa (Marsha Stephanie Blake and Carra Patterson), to decide what to do with it. Each woman has reasons for needing the house: Hannah has a family, and is trying to escape the discriminatory school in which her son is enrolled; and Nessa, despite possessing three degrees, can’t find sufficient work to support herself. But in the first of Greenidge’s twists, the sisters don’t argue endlessly about who live under this roof and why — they’re largely respectful of each other, and sure they can work out something. Assuming, that is, they can find the title.

This might not normally be a catastrophe, but there are some serious doubts about whether Lucy and Rex ever actually owned the house in the first place. In order to acquire it, and move into the upscale neighborhood they’d have otherwise had no access to, Lucy and Rex made a deal with a white family to buy the house for them and sign it over afterwards, in exchange for a considerable sum of extra money. There is, however, no concrete evidence that the second step ever took place, and if it didn’t, Hannah and Nessa’s dreams — to say nothing of Lucy and Rex’s — will never come to fruition.

Greenidge tempers the ensuing detective story by alternating Hannah and Nessa’s scenes with others set in the past, where we witness the troubles that inspired the bargain in the first place. Rex (Victor Williams) is an in-demand surgeon, and Lucy (Eisa Davis) a would-be society scion who has adopted the mien and vocabulary of the born-and-bred Brahmin she’s assuredly not. Joe Donovan (Dashiell Eaves) and his wife Patty Ann (Amanda Quaid), on the other hand, are in many respects the real deal — his parents came over directly from Ireland, and his vocal inflections are pure Kennedy — but are struggling to make ends meet: Joe can scarcely hold down a job, and relies on Patty Ann’s meager laundry business to feed them and their six children. This situation especially rankles Patty Ann, who appears to be the prime motivator for holding onto the title and extorting as much money as possible from the Taylors before relinquishing it.

The core conflict between the families in the 1950s is handled well, as is the messiness that ensues when the better life the Taylors envisioned doesn’t filter down to Nessa, Hannah, or Hannah’s go-along husband Rich (Frank Harts). But much of what surrounds it is schematic, barely even dramatic shorthand for a richer narrative that never materializes. Part of the problem is rooted in pure plot: Everything is set in motion — and, nearly two and a half hours later, arbitrarily halted — through mumbling dialogue scenes between Hannah and the other Joe (Robert Hogan). Such artificial nudges convey little of the urgency Greenidge is trying to impart, a fault made even more glaring by the resolution of the “where” part of the title question that’s so much of an afterthought you might miss it if you blink at the wrong time. The inclusion of whisperings of an interracial romance in the 1950s scenes reek more of theatrical desperation than the repressed longing they’re supposed to represent.

Many of the characterizations are just as sketchy. This isn’t the fault of the actors, all of whom do credible work — and Blake, rooting Hannah’s attitude in an angry neuroticism, and Eaves, who’s positively drenched himself in New England swagger, are particularly engaging. But Rex, Rich, and Joe are functional nonentities, treated for the most part as little more than pawns of the women in their lives — women who too often do not ring true. Lucy’s affectation is practically parodic in how it towers above her husband, to say nothing of the Donovans; and you never sense, as you need to, from either the writing or Davis’s performance that she feels like she should be speaking this way. And Patty Ann is awash in unanchored, one-dimensional rage, the source of which, we learn only in the evening’s waning moments (as acerbically delivered from her future self, played by Jenny O’Hara), is painfully skeletal.

Director Rebecca Taichman has done what she could to mitigate these issues in working with the actors, and the intensity throughout is palpable, though her unimaginative staging on Mimi Lien’s starkly empty set does not help matters. (Justin Townsend’s lights are responsible for carrying the most important scenic weight, and do so admirably.) But the real imagination deficit comes from Greenidge.

She’s cagily adapted real historical events for purposes of exploring how both white and black Americans have traditionally perceived themselves and each other, and unlocks real value in her investigation. But when circumstances demand fiction at least as fascinating as the underlying fact, she does not rise to the challenge. This evening is, in every way, more original, believable, and satisfying than Greenidge’s previous Off-Broadway effort, Milk Like Sugar, which premiered at Playwrights Horizons in late 2011. But it’s almost as heavy-handed and gleeful in selling itself with stereotypical rather than freshly conceived concepts. What’s wrong with Luck of the Irish isn’t the absence of luck, but rather the hard work and sustained creativity that could make such a promising premise explode rather than fizzle.